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Set-Valued Analysis

, Volume 3, Issue 1, pp 71–86 | Cite as

Nonconvex second-order differential inclusions with memory

  • Truong Xuan Duc Ha
  • Manuel D. P. Monteiro Marques
Article

Abstract

We prove several existence theorems for the second-order differential inclusion of the form\(\dot x(t) \in G(x(t)), \ddot x(t) \in - N_{G(x(t))} \dot x(t) + F(t,T(t)x)\) in the case whenF or bothG andF are maps with nonconvex values in an Euclidean or Hilbert space andF(t, T(t)x) is a memory term ([T(t)x](θ)=x(t+θ)).

Mathematics Subject Classifications (1991)

34A60 35K22 

Key words

differential inclusion second-order nonconvex sets normal cones memory 

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Truong Xuan Duc Ha
    • 1
  • Manuel D. P. Monteiro Marques
    • 2
  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Centro de Matemática e Aplicações Fundamentais (CMAF)Universidade de LisboaLisboaPortugal

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